arXiv subjects

Andrew McBride

Publications and source records attributed to Andrew McBride.

14 recordsLinked to original sources

arXiv2026

Unveiling the Multiphysics Complexity: An Isogeometric Framework for Inducing Bifurcation and Tracing Post-Buckling Paths in Electroelastic Thin Shells

Electroelastic shells are widely used in soft actuators, sensors, and energy harvesters owing to their large electrically induced deformations. However, the accurate simulation of their complex nonlinear multiphysics coupling, including bifurcation and post-buckling responses, remains challenging. This work presents an isogeometric Kirchhoff-Love shell formulation for the nonlinear analysis of electroelastic thin structures undergoing finite deformations. The formulation incorporates geometrically nonlinear kinematics, Maxwell-stress-induced electromechanical coupling, material incompressibility, and initial prestretch. Catmull--Clark subdivision surfaces are employed to ensure the C1 continuity required by Kirchhoff--Love shell theory. Consistent tangent operators are derived analytically, and a static condensation procedure is introduced to satisfy the plane-stress constraint. To trace bifurcation and post-buckling equilibrium paths, a staged Newton--Raphson algorithm with arc-length continuation and eigenmode perturbation is adopted. Numerical examples involving spherical membranes, prestretched circular plates, and toroidal membranes demonstrate the capability of the proposed framework to accurately capture large deformations, symmetry-breaking instabilities, and post-buckling responses under coupled electromechanical loading.

math.NA↗

arXiv2026

Inverse Identification of Surface Elastic Parameters in Soft Solids Using GA-ANN Surrogate Model

Surface elasticity plays a crucial role in the mechanics of soft solids at the scale of micrometers and may become significant even at the scale of millimeters in exceptional cases. However, despite the efforts made for the identification of surface elastic parameters, accurately determining these values remains challenging due to the complex interplay with bulk elasticity and nonlinearity. To address this issue, a novel GA-based optimization framework is developed by employing an ANN-based surrogate forward model for efficient identification of surface parameters from the force-displacement response of a cylindrical specimen. The ANN is trained on force-displacement data of a soft cylindrical specimen, generated by nonlinear FE model predictions incorporating model elastic surfaces. The data used for training is generated for non-dimensional values of surface tension in the range of 0-5 and surface shear modulus in the range of 0-50. The accuracy and reliability of the trained ANN are established. The key novelty lies in replacing analytical forward models, which rely on idealized boundary conditions, with a data-driven surrogate trained on FE simulations under realistic constraints. The parameter identification is performed for a number of surface parameter sets using numerically generated force-displacement data as well as for noisy data obtained by adding 5% error in simulated data. The maximum error in identified values of parameters in all the cases is less than 8%. Repeatability and uncertainty analyses based on multiple noisy realizations further demonstrate the robustness of the approach, yielding narrow confidence intervals for the predicted parameters. The proposed framework provides a novel, efficient, and robust alternative to FE-based inverse identification of surface parameters, particularly for experimentally relevant boundary conditions.

physics.comp-ph↗

arXiv2026

Full-Field Damage Monitoring in Architected Lattices Using In situ Electrical Impedance Tomography

Electrical impedance tomography (EIT) enables non-invasive, spatially continuous reconstruction of internal conductivity distributions, providing full field sensing beyond conventional point measurements. Here, we report the first in situ implementation of EIT within a tunable architected lattice materials framework, enabling systematic exploration across a broad lattice design space while achieving real time monitoring of damage evolution, including early stage, prefracture events, in 3D printed multifunctional lattice composites. Lattices are designed via Voronoi based branch trunk branch motifs inspired by 2D wallpaper symmetries and fabricated using CNT infused photocurable resins, with nanoscale filler dispersion confirmed by field emission scanning electron microscopy. Sixteen electrodes distributed along the lattice periphery enable EIT measurements during quasi static tensile loading. Conductivity maps reconstructed using adjacent and across current injection schemes resolve sequential ligament fracture with high temporal resolution, with localised conductivity loss quantitatively coinciding with fracture sites, including regions remote from electrodes. Architectural tunability allows systematic control of EIT imaging sensitivity to early stage damage, while pronounced resistance discontinuities at failure further corroborate spatial localisation; global end to end resistance measurements complement macroscopic stress strain responses. Collectively, these results establish in situ EIT as a scalable, full field sensing modality for architected multifunctional materials, providing an experimentally validated pathway toward autonomous, intelligent materials and data rich material states that can inform digital twin frameworks for structural, biomedical, and energy related applications.

cs.ET↗

arXiv2024

Plane stress finite element modelling of arbitrary compressible hyperelastic materials

Modelling the large deformation of hyperelastic solids under plane stress conditions for arbitrary compressible and nearly incompressible material models is challenging. This is in contrast to the case of full incompressibility where the out-of-plane deformation can be entirely characterised by the in-plane components. A rigorous general procedure for the incorporation of the plane stress condition for the compressible case (including the nearly incompressible case) is provided here, accompanied by a robust and open source finite element code. An isochoric/volumetric decomposition is adopted for nearly incompressible materials yielding a robust single-field finite element formulation. The nonlinear equation for the out-of-plane component of the deformation gradient is solved using a Newton-Raphson procedure nested at the quadrature point level. The model's performance and accuracy are made clear via a series of simulations of benchmark problems. Additional challenging numerical examples of composites reinforced with particles and fibres further demonstrate the capability of this general computational framework.

math.NA↗

arXiv2024

An embedding-aware continuum thin shell formulation

Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour necessitates an understanding of the complex interactions between the structural deformation and the fields in the surrounding medium. For thin shell structures, this challenge is addressed by developing a shell model that effectively incorporates the three-dimensional field it is embedded in by appropriately accounting for the relevant boundary conditions. This study presents a model for the nonlinear deformation of thin hyperelastic shells, incorporating Kirchhoff-Love assumptions and a rigorous variational approach. The shell theory is derived from 3D nonlinear elasticity by dimension reduction while preserving the boundary conditions at the top and bottom surfaces of the shell. Consequently, unlike classical shell theories, this approach can distinguish between pressure loads applied at the top and bottom surfaces, and delivers a platform to include multi-physics coupling. Numerical examples are presented to illustrate the theory and provide a physical interpretation of the novel mechanical variables of the model.

physics.class-ph↗

arXiv2023

A fully-coupled nonlinear magnetoelastic thin shell formulation

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a consistent two-dimensional theory based on a rigorous variational approach. The general deformation map, as opposed to the mid-surface deformation, is considered as the primary variable resulting in a more accurate description of the nonlinear deformation. The commonly used plane stress assumption is discarded due to the Maxwell stress in the surrounding free-space requiring careful treatment on the upper and lower shell surfaces. The complexity arising from the boundary terms when deriving the Euler-Lagrange governing equations is addressed via a unique application of Green's theorem.The governing equations are solved analytically for the problem of an infinite cylindrical magnetoelastic shell. This clearly demonstrates the model's capabilities and provides a physical interpretation of the new variables in the modified variational approach. This novel formulation for magnetoelastic shells serves as a valuable tool for the accurate design of thin magneto-mechanically coupled devices.

physics.class-ph↗

arXiv2022

Computational bifurcation analysis of hyperelastic thin shells

The inflation of hyperelastic thin shells is an important and highly nonlinear problem that arises in multiple engineering applications involving severe kinematic and constitutive nonlinearities in addition to various instabilities. We present an isogeometric approach to compute the inflation of hyperelastic thin shells, following the Kirchhoff-Love hypothesis and associated large deformation. Both the geometry and the deformation field are discretized using Catmull-Clark subdivision bases which provide the C1-continuous finite element framework required for the Kirchhoff-Love shell formulation. To follow the complex nonlinear response of hyperelastic thin shells, the inflation is simulated incrementally, and each incremental step is solved via the Newton-Raphson method enriched with arc-length control. Eigenvalue analysis of the linear system after each incremental step allows for inducing bifurcation to a lower energy mode in case stability of the equilibrium is lost. The proposed method is first validated using benchmarks, and then applied to engineering applications, where we demonstrate the ability to simulate large deformation and associated complex instabilities.

math.NA↗

arXiv2021

Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces

An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialised to infinitesimal deformations and follow the Kirchhoff-Love hypothesis. Both the geometry and physical fields are discretised using Catmull-Clark subdivision bases. It provides the required C1 continuous discretisation for the Kirchhoff-Love theory. The crystalline structure of piezoelectric materials is described using an anisotropic constitutive relation. Hamilton's variational principle is applied to the dynamic analysis to derive the weak form of the governing equations. The coupled eigenvalue problem is formulated by considering the problem of harmonic vibration in the absence of external load. The formulation for the purely elastic case is verified using a spherical thin shell benchmark. Thereafter, the piezoelectric effect and vibration modes of a transverse isotropic curved plate are analysed and evaluated for the Scordelis-Lo roof problem. Finally, the eigenvalue analysis of a CAD model of a piezoelectric speaker shell structure showcases the ability of the proposed method to handle complex geometries.

math.NA↗

arXiv2021

A p-adaptive, implicit-explicit mixed finite element method for reaction-diffusion problems

A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an $H(\mathrm{Div})$-conforming base for the flux vectors, and a non-conforming $L^2$ base for the mass concentration of the species. The mixed formulation captures the distinct nonlinearities associated with the constitutive flux equations and the reaction terms. The IMEX method conveniently treats these two sources of nonlinearity implicitly and explicitly, respectively, within a single time-stepping framework. The combination of the p-adaptive mixed formulation and the IMEX method delivers a robust and efficient algorithm. The proposed methods eliminate the coupled effect of mesh size and time step on the algorithmic stability. A residual based a posteriori error estimate that provides an upper bound of the natural error norm is derived. The availability of such estimate which can be obtained with minimal computational effort and the hierarchical construction of the finite element spaces allow for the formulation of an efficient p-adaptive algorithm. A series of numerical examples demonstrate the performance of the approach. It is shown that the method with the p-adaptive strategy accurately solves problems involving travelling waves, and those with discontinuities and singularities. The flexibility of the formulation is also illustrated via selected applications in pattern formation and electrophysiology.

math.NA↗

arXiv2020

Coupled electro-elastic deformation and instabilities of a toroidal membrane

We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these "reversible" instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.

cond-mat.soft↗

arXiv2020

Modelling the flexoelectric effect in solids: a micromorphic approach

Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. The formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations are derived using the Dirichlet principle and solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this fascinating effect.

physics.class-ph↗

arXiv2020

Assessment of an Isogeometric Approach with Catmull-Clark Subdivision Surfaces using the Laplace-Beltrami Problems

An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace-Beltrami equation requires only C0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull-Clark subdivision surfaces. Catmull-Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull-Clark subdivision surfaces. The performance of the Catmull-Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.

math.NA↗

arXiv2018

Dissipation-consistent modelling and classification of extended plasticity formulations

A unified classification framework for models of extended plasticity is presented. The models include well known micromorphic and strain gradient plasticity formulations. A unified treatment is possible due to the representation of strain gradient plasticity as an Eringen-type micromorphic continua. The classification is based on the form of the energetic and dissipative model structures and exploits the framework of dissipation-consistent modelling to elucidate the flow relation and yield condition. Models are identified as either serial or parallel. This designation is also applicable to familiar models of classical plasticity. Particular attention is paid to the rate-dependent problem arising from the choice of a smooth dissipation potential. The inability to locally determine the region of admissible stresses for the non-smooth (rate-independent) parallel models of plasticity is made clear.

cond-mat.soft↗

arXiv2015

A finite element implementation of surface elasticity at finite strains using the deal.II library

The potentially significant role of the surface of an elastic body in the overall response of the continuum can be described using the mature theory of surface elasticity. The objective of this contribution is to detail the finite element approximation of the underlying governing equations (both in the volume and on its surface) and their solution using the open-source finite element library deal.II. The fully-nonlinear (geometric and material) setting is considered. The nonlinear problem is solved using a Newton--Raphson procedure wherein the tangent contributions from the volume and surface are computed exactly. The finite element formulation is implemented within the total Lagrangian framework and a Bubnov-Galerkin spatial discretization of the volume and the surface employed. The surface is assumed material. A map between the degrees of freedom on the surface and on the boundary of the volume is used to allocate the contribution from the surface to the global system matrix and residual vector. The deal.II library greatly facilitates the computation of the various surface operators, allowing the numerical implementation to closely match the theory developed in a companion paper. Key features of the theory and the numerical implementation are elucidated using a series of benchmark example problems. The full, documented source code is provided.

math.NA↗